Repetitive processes are a distinct class of 2-D systems of both practical and algorithmic interest. The paper gives some important new results on the analysis and control of the sub-class known as discrete linear repetitive processes in the presence of a general set of pass initial conditions, which are termed boundary conditions here. These results consist of stability tests which can be implemented by direct application of standard (or 1-D) linear systems tests and the use of control action to decouple the effects of the boundary conditions.
References
-
-
1)
-
G Peters ,
J.H. Wilkinson
.
The least squares problem and pseudo-inverses.
Comput. J.
,
13 ,
309 -
316
-
2)
-
Smyth, K.J.: `Computer aided analysis for linear repetitive processes', 1992, PhD , University of Strathclyde, Department of Mechanical Engineering.
-
3)
-
D.H. Owens
.
Stability of linear multipass processes.
Proc. Inst. Electr. Eng.
,
11 ,
1079 -
1082
-
4)
-
P.D. Roberts
.
Stability analysis of iterative optimal control algorithms modelled aslinearrepetitive processes.
IEE Proc. Control Theory Appl.
,
3 ,
229 -
238
-
5)
-
K. Galkowski ,
A. Gramacki ,
J. Gramacki ,
S.G. Tzafestas ,
G. Schmidt
.
(1998)
Analysis of properties of multitime scale systems in 2-D approach, Progress in system and robotic analysis and control design.
-
6)
-
Rogers, E., Gramacki, J., Galkowski, K., Owens, D.H.: `Stability theory for a class of 2-D linear systems with dynamic boundaryconditions', Proceedings of 37th IEEE International Conference on Decision and Control, December 1998, p. 2800–2805.
-
7)
-
E. Rogers ,
D.H. Owens
.
(1992)
Stability analysis for linear repetitive processes, Lecture Notes in Control and Information Sciences Series.
-
8)
-
N. Amann ,
D.H. Owwens ,
E. Rogers
.
Iterative learning control using optimal feedback and feedforward actions.
Int. J. Control
,
2 ,
277 -
293
-
9)
-
M. Araki ,
K. Yamamoto
.
Multivariable multirate sampled-data systems: state-space description,transfer characteristics, and Nyquist criterion.
IEEE Trans. Autom. Control
,
2 ,
145 -
154
-
10)
-
Roberts, P.D.: `Unit memory repetitive processes and iterative optimal control algorithms', Proceedings of International Conference Control 94, Warwick, UK, p. 454–459.
-
11)
-
E. Fornasini ,
G. Marchesini
.
Doubly-indexed dynamical systems: state space models andstructural properties.
Math. Syst. Theory
,
59 -
72
-
12)
-
R.P. Roesser
.
A discrete state space model for linear image processing.
IEEE Trans. Autom. Contr.
,
1 ,
1 -
10
-
13)
-
K. Galkowski ,
E. Rogers ,
D.H. Owens
.
Matrix rank based conditions for reachability/controllabilityof discrete linear repetitive processes.
Lin. Algebr. Appl.
,
201 -
224
-
14)
-
J.B. Edwards
.
Stability problems in the control of multipass processes.
Proc. Inst. Electr. Eng.
,
11 ,
1425 -
1431
-
15)
-
J.L. Aravena ,
M. Shaflee ,
W.A. Porter
.
State models and stability for 2-D filters.
IEEE Trans. Circuits Syst.
,
12 ,
1509 -
1519
-
16)
-
N. Amann ,
D.H. Owens ,
E. Rogers
.
Predictive optimal iterative learning control.
Int. J. Control
,
2 ,
203 -
206
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